Designed Patterns: Flexible Control of Precipitation through Electric Currents

Understanding and controlling precipitation patterns formed in reaction-diffusion processes is of fundamental importance with high potential for technical applications. Here we present a theory showing that precipitation resulting from reactions among charged agents can be controlled by an appropriately designed, time-dependent electric current. Examples of current dynamics yielding periodic bands of prescribed wavelength, as well as more complicated structures are given. The pattern control is demonstrated experimentally using the reaction-diffusion process $2{\mathrm{AgNO}}_3+{\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7\to \underline{{\mathrm{Ag}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7}+2{\mathrm{KNO}}_3$.

Figure 1

Experimental setup for producing Liesegang precipitation patterns as described in the text. The controlling agent is the generator providing electric current $I(t)$ with a prescribed time dependence.

Figure 2

Concentrations of the reaction product in the wake of the front, in the absence of a current, respectively, when a constant forward or backward current, or a quasiperiodic current (changed at times $\tau n^2/2$) is switched on [19].

Figure 3

Theoretical precipitation patterns. The periodic pattern emerging in the presence of a quasiperiodic current (upper panel) as compared to the usual Liesegang band-structure obtained in the absence of current (lower panel). The values $c_h$ and $c_l$ are the stable concentrations of $C$ [19].

Figure 4

Experimental precipitation patterns. A quasiperiodic current of amplitude $500\mu \mathrm{A}$ was used with $\tau =4$, 2, and 1 min, respectively, as going down the panels. Lowest panel illustrates the usual Liesegang bands.

Figure 5

Characteristic wavelength $d$ of the pattern generated experimentally by switching the current forward and backward at times $\tau n^2/2$. The front diffusion coefficient $D_f$ is the result of a linear fit.

Figure 6

An example of a predesigned pattern. The protocol described in the text for generating the “2-3-2” structure is shown to work both in the experiment (upper panel) and in the theory (lower panel) [19].